A heavy ball of mass m is attached to a light but rigid rod of length L . The rod is pivoted at the top
and is free to rotate in a circle in the plane of the page, as shown above.(a) The mass oscillates to a maximum angle θ . On the picture of the mass m below, draw a vector
representing the direction of the NET force on the mass while it is at angle θ . Justify your choice
of direction.
(b) Is the magnitude of the net force at the maximum displacement equal to mg sinθ or mg cosθ ?
Choose one and justify your choice.
(c) Derive an expression for the ball’s potential energy U as a function of the angle θ . Assume that a
negative angle represents displacement from the vertical in the clockwise direction.
(d) On the axes below, sketch a graph of the mass’s potential energy U as a function of the angle θ for
angles between −90° and +360°. Label maximum and minimum values on the vertical axis.
(e) The pendulum is considered a classic example of simple harmonic motion when it undergoes
small-amplitude oscillation. With specific reference to the graph you made in part (d), explain
why the assumption of simple harmonic motion is valid.
STOP. End of Physics C—Mechanics Practice Exam—Free-Response Questions